Here you will find information about the material that was already covered or will be covered in the next few lectures.

Covered  
Fri, Apr 19: [M] §30 The Differential Operator, §32 The Action of a Differentiable Map
Mon, Apr 17: Overview of Midterm Exam 2
Mon, Apr 15: [M] §29 Tangent Vectors and Differential Forms
Fri, Apr 19: [M] §27 Alternation Tensors, §28 Wedge Product
Wed, Apr 17: [M] §26 Multilinear Algebra, §27 Alternation Tensors
Mon, Apr 15: Review for Midterm Exam 2
Fri, Apr 12: [M] §25 Integration of a Function over a Manifolds
Wed, Apr 10: [M] §24 Examples, §25 Integration of a Function over a Manifolds (start)
Mon, Apr 8: [M] §24 The Boundary of a Manifold
Fri, Apr 5: [M] §23 Manifolds in $\mathbb{R}^n$ (cont.)
Wed, Apr 3: [M] §16 Partitions of Unity (cont.) §23 Manifolds in $\mathbb{R}^n$
Mon, Apr 1: [M] §16 Partitions of Unity
Fri, Mar 29: [M] §15 Exhaustion by Compacts, Improper Integrals, §16 Bump Functions
Wed, Mar 27: [M] §22 Volume of a Parametrized Manifold, Integration on a Parametrized Manifold
Mon, Mar 25: [M] §21 Volume of the Parallelopiped
Fri, Mar 22: [B] §45 Change of Variables (Strong Form)
Wed, Mar 20: [B] §45 Change of Variables
Mon, Mar 18: [B] Overview of Midterm Exam 1, §45 Transformation by Nonlinear Maps, Jacobian Theorem
Fri, Mar 15: Spring Break
Wed, Mar 13: Spring Break
Mon, Mar 11: Spring Break
Fri, Mar 8: Cancelled (because of Midterm Exam 1)
Wed, Mar 6: [B] §45 Transformation by Linear Maps, Transformation by Nonlinear Maps (start)
Mon, Mar 4: [B] Review for Midterm Exam 1
Fri, Mar 1: [B] §45 Transformations of Sets with Content
   
Wed, Feb 27: [B] §44 Integral as Iterated Integral, §45 Transformations of Sets with Content (start)
Mon, Feb 25: [B] §44 Further Properties of Integral, Mean Value Theorem
Fri, Feb 22: [B] §44 Sets with Content (cont.), Characterization of Content Function
Wed, Feb 20: [B] §43 Properties of Integral (cont.), Existence of Integral, §44 Sets with Content (start)
Mon, Feb 18: [B] §43 Darboux’s upper and lower integrals (cont.), Riemann’s Criterion for Integrability, Properties of Integral
Fri, Feb 15: [B] §43 Definition of Integral, Darboux’s upper and lower integrals (Project 43.$\alpha$)
Wed, Feb 13: [B] §43 Content zero
Mon, Feb 11: [B] §42 Inequality Constraints, Examples
Fri, Feb 8: [B] §42 Lagrange’s Theorem (finish), Examples
Wed, Feb 6: [B] §42 Second Derivate Test (finish), Extremum Problems with Constraints, Lagrange’s Theorem (start)
Mon, Feb 4: [B] §42 Local (Relative) Extrema, First Derivative Test, Second Derivative Test (start)
Fri, Feb 1: [B] §41 Implicit Function Theorem
Wed, Jan 30: Cancelled (Wind Chill Emergency)
Mon, Jan 28: [B] §41 Inversion Theorem, Implicit Function Theorem (start)
Fri, Jan 25: [B] §41 Surjective Mapping Theorem, Open Mapping Theorem
Wed, Jan 23: [B] §41 Class $C^1$, Approximation Lemma, Injective Mapping Theorem
Mon, Jan 21: No class (MLK day)
Fri, Jan 18: [B] §40 Higher Derivatives, Taylor’s Theorem, §41 Class $C^1$ (start)
Wed, Jan 16: [B] §40 Interchange of the Order of Differentiation
Mon, Jan 14: [B] §40 Chain rule, Mean Value Theorems
Fri, Jan 11: [B] §39 Jacobian, existence of the derivative, §40 Algebraic properties of derivatives
Wed, Jan 9: [B] §39 Directional and partial derivatives, the derivative
Mon, Jan 7: [B] §39 The Derivative (start), §21 Linear functions